TakenItSeriously

It comes down to choosing from which point of view you want to look at a problem from. The observer you choose is typically assumed to be stationary relative to the other inertial frame. If need be, you can then swap observers to get another other point of view.

I'm having a tough time getting a laypersons understanding for the differences between: covariants, contravariants, invariants, and variants as they relate to Lorentz transforms in the field of Special Relativity. An intuitive definition for those terms would be wonderful, but I'd be extremely grateful even for some examples of each. They don't need to be limited to the field of SR, but if outside of that field such as a references to GR instead, please be sure to list it as such. Thanks.

.In SR, acceleration is the equivalent to gravity, which might be the answer you're looking for. But to answer your question about the source of the Lorentz shift. It doesn't come from gravity, it's more of a mathematical relationship that predates relativity. I'm not certain of it's history, or original purpose, but it essentially is a kind of exponential scale factor. The fact that it is used in both GR and SR may not be a coincdence, but it's application is not the same. In GR, it's based upon the properties of gravity. In SR, it's based upon the properties of velocity. Therefore the mechanisms for it's use are very different. Figure 1 & 2: The graph on the left shows the degree of impact the Lorentz factor plays as the scales of velocity approach c. The graph on the right right shows the inverse of the Lorentz factor with respect to the ratio of v/c. It's interesting to note that some would say that the graph on the right shows that the change in speed relative to an outside observer is related to a dimensional shift or rotation in spacetime.

.You can think of it like this. Imagine the rocketship is moving away from the Earth at 0.8c while transmitting a 100 GHz clock signal, in dilated time. The wave front must still travel back twoards the Earth at c, but time has slowed the transmitting frequency down to 60GHz. On top of this, the regressive speed of the ship may not impact c, but it still enhances the doppler effect, slowing it down to 36 GHz. .The easiest way to visualize that gravity could not be the source of the time deviation is that we know that the deviation changes in direct proportion to the distance. Therefore it's source must be form an inverse Lorentz shift, which is a linear relationship. Gravity or acceleration, on the other hand both operate through exponential curves due to the squared factor, and behave nothing like linear relationships.

This sounds a lot like relativistic dopler shift. When we approach the SOL relative to another inertial frame such as the Earth frame, then earthlings would see light from our ship turn red and due to its frequency slowing down as well as our time slowing down. But light is actually photons carried by EM waves. However, I believe that the redshift is in part an effect of time dilation rather than the other way arround..

.Understanding the Twin Paradox is only as important as you need it to be. However if you are a theoreticle physicist, then It's probably worth the time to make certain you understand it, because you cannot move forward very easily if one doesn't understand what one thinks they already know. In fact, until any problem suddenly collapses into a very simple solution, you probably don't fully understand the problem. There may be hundreds or even thousands of valid but worthless solutions, because they don't teach you anything about the problem. There is only one other solution that can be found through Relativistic doppler effect which some physicists consider to be the predominant solution. Its a valid solution, but the ultimate source and the most elegant solution is length contraction. I'm pretty sure relativistic doppler effect gets it's information from length contraction. The simplest solutions are only the simplest in hind site, but they are very difficult to find in fore-site. In this case it involved understanding the symmetry of SR being twisted by 90⁰ as a consequence of c being constant. It's like a riddle I posted not long ago based upon a poker home game that you host for many players of different skills while you keep a complete database of every hand ever played. Someone asks you what the average players win rate is. You decided to figure it out and work for hours on finding the answer. But then you still suddenly know the answer, and kick yourself because it's so simple. The thing is, it's not a simple answer to find only simple in hind site. It was only easy to find because you figured out the problem. Finding some good enough solution that doesn't tell you anything won't help either. .Only if length contraction was included as part of your method. Which is very often the case, because its required to work through the entire problem. Or just remove length contracrion from the problem and see if the solution resolves itself down to 0 time difference to prove how many sources there are. .It does but length contraction is symmetrical between frames just like time dilation is. The two frames being the [ship's] frame and the [Earth + spacetime +star system] frame. So the ship contracts from the POV of earth bound twin, and the earth frame contracts from the POV of the traveler. BTW: There is still a key piece missing from SR symmetries that I'm trying to create a convincing enough argument for because it requires making a minor change to SR, which I doubt will be accepted no matter how convincing or clear I make it. It's a minor issue to SR but in a way it unifies cosmology with SR.

I think it amounts to not negotiating with terrorists. Once the policy is set the potential damage from future crime becomes the greater concern. Besides, once it is known that a cure for cancer is possible, then finding it again becomes so much easier because you have removed all doubt about finding it eventually.

I recently discovered a new Twin Paradox video that had been posted on YouTube "The Twin Paradox visualized in Special Relativity" https://youtu.be/ifRuWG98ATY It was posted 6 days after I had posted the OP to this thread which may be an original solution based on what I've been able to Discover. In it he used my solution as one of three solutions claiming that there were several valid solutions that could work. This is simply not true. Why length contraction or it's equivalent is the only valid solution Nearest star system: distance: d = 4 light years away Ships speed v = 0.8c Earths Perspective: d = 4 light years t = 2d/v = 8/0.8 = 10 years Travelers Perspective: Lorentz factor: ε = 0.6 d = 0.6 * 4 = 2.4 light years t = 2 * 2.4/0.8 = 6 years The unintuitive results are due to the lorentz factor: γ = 1/sqrt[1-(v²/c²)] The only relavent variables involved in this factor are those that relate to speed which are distance and time. Since time is always symmetrical we are left with only distance as the source of the asymmetrical result. Therefore length contraction must be the source of the time difference experienced by each twin. The Earth bound twin observes the ship travel 8 light years in 10 years. The ship bound twin only travels 60% of the distance which takes 60% of the time or 6 years. Invalid solutions : Stepped through the timeline showing all details at each step in order to show the symmetrical observations vs the asymmetrical results. This is only showing that length contraction is the source of the dime deviation. Remove length contraction and time does not deviate. Another solution also goes through all of the details and conclude with the following statement: "The asymmetry in the paradox is that the traveler leaves the earth?s reference frame and comes back, whereas the homebody never leaves the earth" Which says nothing at all but that the traveler left at a relativistic speed and returned at a relativistic speed while the earth twin stayed on earth. Its just a restatement of the problem. Lots of others state its the acceleration, but acceleration doesnt scale. If you traveled 8 ly or 80 lys the acdeleration would be identical at 100days but the delta time is ten x as much. One solution mentioned it had to do with the relatavistic dopler shift + something else. The details were never given for that solution but dopler shift is essentially caused by length contraction.

Create a kind of shunt birth control technology that could be open/closed using encrypted near-field signals to eliminate unplanned pregnancy. If needed, once it becomes a proven, safe, and economically feasible enough, make it a mandatory, government sponsored proceeder. If needed, regulate the birth rate to be fixed at x per person granted to people at birth, where x does not need to be an integer and birth credits can be traded on the open market. Details should be a separate discussion but with the goal being x = 1 once a sustainable population is achieved.

They had generations and countless numbers to continuously practice, improve and perfect their techniques. Experience will always be the key factor. I'm sure they had smart and innovative people in the past as well. No reason to think we should be able to duplicate their methods that easily today without the benefit of their experience.

It sounds like the OP is trying to generate a best of list for nuggets of wisdom that had the greatest positive psychological impact on either individuals or humanity.

Very close to the solution I had chosen to show. Their are a few minor variations possible. But they will always be solved in 3 tests.

Not bad, 50% 4bal, 50% 3bal depending on 2nd result. Not the best though. All future solutions should be placed within spoiler tags, thanks.

There are 12 golf balls in a box. You know that one flawed ball accidentally got mixed into the batch. The flaw is that the weight is off but you don't know if it is too heavy or too light. You can only detect the flaw through the use of a balance (not a scale) that can only detect which of two trays contents is heavier. Describe the most efficient method (fewest number of balances) to identify the flawed ball. To help you describe the method use the following codes: U = Untested L = golf ball from a Lighter group H = golf ball from a Heavier group E = golf ball from an equal or balanced result (good golf ball). Example: After balancing 6U vs 6U you get 6L & 6H Please put solutions within spoiler tags 1) find the most efficient method P.S. I believe It should be possible to prove if a method is optimal but I haven't validated my method for testing optimal conditions yet so 2) comes with no guarantees for an answer. 2) prove it's the optimal method

Since mixing was added to the riddle after the fact we will use a wooden stir stick with negligible conduction properties. Also assume the agitation created by stirring has negligible effect on cooling through convection and adds negligible energy to brownian motion.

Given that the vast majority of the population share the same incorrect illusion, I would hardly think its something unique to my mind and finding a solution would be of particular value for being able to judge the validity of future axioms. Also, I dont think anyone who actually read the solution disputes its correctness. Never the less I gave a method for proving the solution to yourself which would take deck of cards and about 20 seconds to verify.

Also it is generally better to keep it down to two observers. Adding a third observer, especially if they are directly between the other two can create additional confusion since the middle observer combining the speeds of the other two wont be consistent with the speeds the other two are observing between each other. For example if two people are approaching the center observer at 0.6c from opposite directions then the middle observer might incorrectly deduce that they are moving at 1.2c relative to each other while they would both experience the other approaching at a speed less than c

Solution:

Yes, they are also known as Minkowski diagrams. I don't think so. And why would you want to if you can get the time dilation by using any inertial frame, and in particular the rest frame of the twin on earth? It's just how the paradox is constructed. Or at least one version of it, which I'm just now realizing, could be our disconnect in this thread and which I should have made more clear, so I apologize if such is the case. The original and more widely known version only talks about the apparent paradox being that the twins end up being different ages. However there is another version of the paradox that includes symmetrical observations made by the twins and goes something like the following: Assume each twin had a local clock such as a powerful spotlight that would revolve once a second so that the other twin could see it flash on each rotation using a telescope. Both twins would observe their brothers local clock slowing down by the same amount on the trip out and on the return leg they would both observe that the others local clock would speed up by the same amount. So the paradox goes: with symmetrical observations by both twins over their brothers passage of time, how do we explain the 4 year difference in the twins in time experienced. If you look only at the time that has passed by in either twins frame, it's providing self-consistent information and resolves the first version of the paradox, but it's a bit redundant to saying they experienced a different amount of time and doesn't resolve the paradox as it was constructed here. To resolve the second form of the paradox the solution must include the data that isn't symmetrical by virtue of the destination always being stuck to the Earth's inertial frame. And that data which is always different from either of the twins reference frames is the distance they each felt was covered by the rocket. The Earth bound twin would say he saw it cover 8 light years in ten years. The traveling twin would say he traveled 5.2 light years in six years.

You mean Minkowski diagrams? Sorry If Im a little slow. Im not a physicist so Im not used to all of the methods and common references. But couldn't you create the same kind of symmetry by redefining which frame is moving? Then it comes down to breaking symmetry by changing the travelers reference frame several times and starting and ending up on the earth frame, but it's leads to a pretty non-specific resolution which seems to be the source for all of the confusion. The distances covered are never the same value regardless of who is moving because the destination always moves with the earth frame and never with the ships frame.

So are you talking about using the Lorentz transform tor time as a kind of scale conversion factor for the earth frame? Example If the Lorentz factor is 0.6 T = 0.6 * 4/0.8 = 3 years passed on the spaceship to the planet, 6 years round trip And T = 4/0.8 = 5 years passed on the earth to get to the planet, 10 years round trip I'm not certain, but that could be seen as circular reasoning if your trying to resolve the paradox. The apparent paradox is that you can run the same exact transform for both twins in both directions and the results appear to be symmetrical. Using the distance they each thought was traveled breaks symmetry because they would be different values.

I wasn't trying to take a position, only trying understand your reference. When you mentioned electric field, I was thinking in terms of charged particles that moved in a parabola, but the only reference Ive seen for dipoles would be to create a torque on their dipole moments causing them to polarize. The path of the particle doesn't deviate because their wouldn't be a net force in either direction that would cause them to deviate. The effect you seemed to be talking about is an electrostatic effect which is a small effect that is similar but not necessarily the same as when you rub a balloon on a sweater. The water reference was when an electrostaticaly charged plastic comb could be used to deflect a slight flow of water out of a tap. I'm not so sure that there is a single accepted explanation for the effect, as each article I found had pointed out different misconceptions about the effect. Some stating ion impurities in the water, another stating that it was due to a non uniform electrostatic field which didn't help me with the understanding much. Others stating it had to do with H2O dipole moments and others claiming it would effect any material with a strong enough field. Of course, these effects are at a relatively static state and the speed of light is at the other extreme and takes something more than a static field. HSD or High Speed Design, is the study and treatment of high frequency signal waves in a Printed Circuit Board Domain as they change from behaving like DC circuits to behaving like AC circuits (alternating voltage). It's a relatively new field where digital design underwent a paradigm shift in the 90s due to the signal frequencies becoming too fast in terms of frequency, relative to the speed of light, causing Printed Circuit Boards to fail while digital design engineers couldn't understand why. Simply put, high speed digital waves propagate through EM fields within the substrate material of a PCB at the speed of light (6"/ns for FR-4) and they are carried by photons, just like light waves. Also digital signal waves aren't really square waves, they are only approximations of square waves created by combining odd harmonics of sine waves. Once the signal transition time fits within the length of the trace as defined by the speed of light (that converts length into time) then you need to treat them very differently. One of the fundamental effects is that instead of following the path of least resistance, a signals return path through a ground (or power) plane is the path of least impedance which is typically directly under the signal trace. Another words, the waves carried by photons will follow a curved path, not a straight line. How much they curve is dependent upon the frequency. I haven't heard of NMR Spectroscopy but I will look it up, thanks. My interest in photons being dipoles could be enough to explain their self propagating through a vacuum which I think the current model fails to do. If they were able to orbit each other as differential pairs, where their dipole moments would cause them to orbit, then they would be self propagating. Imagine a photon moving in a helical motion, then the EM waves would be the perpendicular projections of the wave. Only a single photon wouldn't orbit itself. If photons were dipoles, then two of them could propagate in a dual helical motion and their EM waves would then be differential. Differential waves are self probagating, also they don't require a reference, since they are self referencing. On the left is the model for a particle helix I was thinking about. Unfortunately I don't have a gif for a dual helix that creates differential waves. You have to imagine a second helix and differential sine waves that are 180⁰ shifted to each other. On the right is a model of a differential pair where the arrows represents the EM field and the black dots show the motion of the electrons. Note the helical shape. Unfortunately both images are much better representations as animated gifs, which I don't know how do post.

I'm not familiar with the method you described but it sounds like it involves a lot of conversions between frames which, I think, is where most people seem to get confused. Ive seen proofs thinking it was due to acceleration, and another proof that seemed to think it was resolved on the return trip, and others that say it has to do with jumping reference frames. The last one is true but not very specific and jumping reference frames makes it sound like it's about acceleration, which it's not. If you simply asked each twin what they thought the distance traveled was, they would give you two different answers that were different by 60%

There is no paradox, that's only what the problem is known as. Im just showing that the solution has nothing to do with time Dilation. Read the post. I changed the title to "Why time dilation has nothing to do with solving the Twin Paradox" so as to not mislead anyone.

The twin paradox is created by both the twin on the ship and the twin on the earth seeing the other persons clock change by the same amount, therefore there doesnt seem to be a way to account for the age difference when they meet up after the voyage. Edit to add: The paradox is not just the fact that the twins are different ages at the end. Its that they have symmetrical observations about each others passage of time and still have a difference in time experienced. Read post # 11 for a better explanation of the specific paradox I'm talking about. First of all, I will use the example from the Wikipedia article about the twin paradox so that I can highlight the facts to make the problem as transparrent as possible without involving too much explanation and you can verify those facts by reading the article. Secondly, I will point out that the destination star system is not moving in reference to the Earth. At least not based on the calculations that were used. Thirdly, I won't mention anything about time dialation because time dialation has nothing to do with the problem. Neither does the relative motion of the destination for that matter, except for easier visualization of the problem. Example: Consider a space ship traveling from Earth to the nearest star system: distance d = 4 light years away, Ships speed v = 0.8c Assume Acceleration time is negligible. Earths Perspective: d = 4 light years t = 2d/v = 8/0.8 = 10 years Travelers Perspective: Lorentz factor: ε = 0.6 d = 0.6 * 4 = 2.6 light years t = 0.6 * 2d/v = 0.6 * 10 = 6 years So the solution to the paradox is that traveling 60% of the distance takes 60% of the time. It's that simple. The earth twin observes the ship traveling a total of 8 light years in ten years at 0.8c. The traveling twin thinks he only traveled 5.2 light years in 6 years at 0.8c The illusion of the paradox is created by people assuming that only the length of the ship is contracted which isn't correct. Just as with time dilation working both ways making the problem seem paradoxical, so does length contraction work both ways which resolves the paradox. The length of the ship is contracted only relative to the observers on Earth, not to the traveler on the ship. To the traveler, it is the distance between the Earth and the destination is what is being contracted because they share the same inertial reference frame. If you need to, imagine a very long stick suspended between the two points. Then to the traveler on the ship, the stick, the Earth and the destination star system system are all moving as one system at 80%c therefore the traveler sees that entire system contract by 60%. So what happens if the destination is moving relative to the Earth? Nothing much exept the math needs to account for the difference just as if you were taking a speed boat from a dock to a moving ship in the distance and back. The distance traveled at 80%c is still going to be 60% of the distance that the observers on the Earth believe was traveled. That's because what ever the point of contact between the ship and the destination, be it 4 light years away or 4 billion light years away one could always imagine that point being a static point relative to the Earth. Think of it like a timing play where the quarter back throws to a spot on the field instead of throwing to a running receiver. The field would be the inertial reference frame.